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A125826 Numbers m that divide 2^7 + 3^7 + 5^7 + ... + prime(m)^7.

%I A125826 #63 Jan 17 2024 07:43:45
%S A125826 1,25,1677,21875,538513,1015989,18522325,1130976595,1721158369,
%T A125826 561122374231,1763726985077,2735295422833,7631117283951,
%U A125826 22809199833151,46929434362563,49217568518075,151990420653423,174172511353413,1258223430425543
%N A125826 Numbers m that divide 2^7 + 3^7 + 5^7 + ... + prime(m)^7.
%C A125826 See A232865 for prime(a(n)). - _M. F. Hasler_, Dec 01 2013
%C A125826 a(17) > 5.5*10^13. - _Bruce Garner_, Aug 30 2021
%C A125826 a(18) > 1.56*10^14. - _Paul W. Dyson_, Mar 02 2022
%C A125826 a(19) > 1.9*10^14. - _Bruce Garner_, Sep 18 2022
%H A125826 OEIS Wiki, <a href="https://oeis.org/wiki/Sums_of_primes_divisibility_sequences">Sums of powers of primes divisibility sequences</a>.
%t A125826 s = 0; Do[s = s + Prime[n]^7; If[ Mod[s, n] == 0, Print[n]], {n, 25000}]
%o A125826 (PARI) s=0; n=0; forprime(p=2, 4e9, s+=p^7; if(s%n++==0, print1(n", "))) \\ _Charles R Greathouse IV_, Mar 16 2011
%Y A125826 Cf. A232865.
%Y A125826 Cf. A085450 (smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n).
%Y A125826 Cf. A007504, A045345, A171399, A128165, A233523, A050247, A050248.
%Y A125826 Cf. A024450, A111441, A217599, A128166, A233862, A217600, A217601.
%K A125826 hard,nonn
%O A125826 1,2
%A A125826 _Alexander Adamchuk_, Feb 03 2007
%E A125826 More terms from _Ryan Propper_, Mar 26 2007
%E A125826 a(8)-a(9) from _Charles R Greathouse IV_, Mar 16 2011
%E A125826 a(10) from _Paul W. Dyson_, Jan 05 2021
%E A125826 a(11)-a(12) from _Bruce Garner_, Feb 26 2021
%E A125826 a(13) from _Bruce Garner_, Mar 23 2021
%E A125826 a(14) from _Bruce Garner_, May 19 2021
%E A125826 a(15)-a(16) from _Bruce Garner_, Aug 30 2021
%E A125826 a(17) from _Paul W. Dyson_, Mar 02 2022
%E A125826 a(18) from _Bruce Garner_, Sep 18 2022
%E A125826 a(19) from _Paul W. Dyson_, Jan 17 2024